In the receiver of a contemporary digital communication system, an equalizer operates to compensate for various forms of distortion introduced by the propagation medium. In wireless communication systems for example, an important source of such distortion is time-varying multipath propagation, whereby the transmitted signal travels through multiple paths en route to the receiver due to reflections off objects in the propagation environment. In wireline communication, such as twisted copper wire pair or co-axial cable, such distortion arises due to the frequency response characteristics of the physical medium, referred to herein as the “channel”, or of other system hardware in the network.
Absent some form of correction or compensation, such distortion can cause streams of transmitted bits or symbols to interfere with one another, a phenomenon generally referred to as intersymbol interference. In certain code-division multiple-access (CDMA) communication systems, distortion may further give rise to a phenomenon referred to as inter-chip interference. Intersymbol interference (ISI) is used herein to refer to both forms of interference. Precursor ISI is caused by the strictly anticausal portion of the equivalent discrete-time channel impulse response, whereby a current symbol affects symbols in the past. Postcursor ISI is caused by the stricly causal portion of the equivalent discrete-time channel impulse response, whereby a current symbol affects symbols in the future. ISI can lead to severe degradation in system performance, especially in wireless settings. Equalizers, designed to compensate for, and to mitigate the effects of, such interference, have been under development for more than three decades and have evolved to become essential components in virtually all modern communication systems.
It is well known in theory that receivers that realize maximum-likelihood sequence detection (MLSD) are asymptotically optimal in bit-error rate at high signal-to-noise ratios (SNR), as observed in G. D. Forney, Jr., “Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference,” IEEE Trans. Inform. Theory, vol. IT-18, pp. 363-378, May 1972. However, even when implemented efficiently using the Viterbi algorithm, the computational requirements of such receivers are prohibitive for even small signal constellations and channels whose ISI spans only a modest number of symbols. Indeed, although the complexity of MLSD is independent of block-length, it does grow as ML−1 where M is the size of the symbol alphabet and L is the length of the impulse response of the equivalent discrete-time channel. As a result, practical equalizers rarely employ MLSD.
Two approaches have become popular in practice: linear equalizers (LEs) and decision-feedback equalizers (DFEs). LEs were developed in the 1960's, and employed linear filters to compensate for distortion. Later, in the late 1960's and early 1970's, the inherently non-linear DFEs were introduced. In both cases, the computational complexity is dramatically lower than the theoretically superior MLSD approach—it is essentially independent of the size of the symbol alphabet M and proportional to the length of the channel impulse response L.
Like the LE, the DFE processes the received signal using a linear filter and makes symbol decisions using a slicer, as disclosed in C. A. Belfiore and J. H. Park, Jr., “Decision-feedback equalization,” Proc. IEEE, vol. 67, pp. 1143-1156, August 1979. However, each time a decision is to be made, a linear, strictly causal filter forms a weighted linear combination of previous symbol decisions, assumed to be correct, to cancel the postcursor ISI at the slicer input. The slicer then generates a decision for the current symbol. Note that once a symbol decision is made, it does not change and is used to cancel postcursor ISI when making decisions for future symbols.
Another equalizer approach, referred to as the “ISI canceler”, processes the received signal using a linear filter and makes symbol decisions using a slicer, as disclosed in Gersho and T. L. Lim, “Adaptive cancellation of intersymbol interference for data transmission,” Bell Syst. Tech. J., vol. 60, pp. 1997-2021, November 1981. However, each time a decision is to be made, a linear noncausal filter forms a weighted linear combination of both previous and future tentative symbol decisions made by some other equalizer, typically a linear equalizer, to cancel ISI at the slicer input. The slicer then generates a final decision for the current symbol.
LEs are widely used, but often suffer from excessive noise enhancement, even when minimum mean-square error (MMSE) design criteria are used. DFEs are capable of better performance, particularly at higher SNR, because postcursor ISI is suppressed nonlinearly. However, noise enhancement is still an issue in DFEs because precursor ISI is only suppressed linearly, and the sequential structure of DFE algorithms make them generally incompatible with error-control channel coding due to decoding delay issues, despite numerous attempts to merge the two; see, for example, (a) J. G. Proakis, Digital Communications. New York, N.Y.: McGraw-Hill, 2nd ed., 1989. (b) V. M. Eyuboglu, “Detection of coded modulation signals on linear, severely distorted channels using decision-feedback noise prediction with interleaving,” IEEE Trans. Commun., vol. COM-36, April 1988. (c) K. Zhou and J. G. Proakis, “Coded reduced-bandwidth QAM with decision-feedback equalization,” in Proc. Int. Conf. Commun., pp. 12.6.1-12.6.5, June 1988. (d) K. Zhou, J. G. Proakis, and F. Ling, “Decision-feedback equalization of fading dispersive channels with trellis-coded modulation,” in Proc. Int. Conf. Commun. Techn., November 1987. Since error-control coding is required to approach channel capacity, an equalizer compatible with this feature is highly desirable.